Just an intuitive understanding that if we decrease infant mortality we will net the human race many more years of life than anti-aging research. Spare a few cents for a vaccine anyone? As opposed to dumping a bunch of money into theoretical anti-aging efforts.
Now you might argue that one additional year for an adult is more valuable to society than one additional year for a child, but I'd rather not quibble over the exact value of a year of life. There are counterarguments; how many genius do you think we lose in Africa because of inadequate medicine and education?
EDIT: If it's cheaper than optimizing on the low end, then of course I would support optimizing on the high end. But given the large number of human beings that die young for stupid reasons, I can't imagine that the high end is cheaper. Thanks for pointing out Aubrey de Grey, though. I'll do some reading.